Just throwing in my $0.02.
The above procedure is yeast rinsing. Washing involves acids & removing bacteria/other microbes. Rinsing is getting the trub & less desirable yeast out of your slurry. If your yeast has gone sour on you, rinsing won't help. Actual yeast washing at our level & with the tools that most of us have is rather difficult - it can be done, but from my experience playing with it, it's not worth the hassle. The only thing I would add to the otherwise excellent explanation of rinsing above is that you want to pour off the top layer as well - let it settle, pour off top 'thin' layer, decant off from bottom layer.
What I found to be extremely helpful was to use a canning kettle. I put in as many mason jars in the bottom that will fit, fill with water until you have an inch or 2 above the mouths of the jars. Bring to a boil for at least 4 minutes to completely sterilize both water & jars. As soon as the boil begins I also put my metal kitchen tongs in there (vertically, with the handle sticking out of the kettle). I reduce heat when the timer goes off & use the tongs to remove the jars, pour out ~1/2 the water & cover with foil while they cool. The boil sterilizes the tongs, water & jars. The steam sanitizes the foil. When they're cool to the touch I cap them with StarSan soaked lids & have a nice supply of sterile water in the fridge. Then you just have the opposite to remember - instead of letting your pre-boiled water cool to rinse your yeast, you need to remember to remove the jar from the fridge early enough to come to room temp. Yeast shock is yeast shock.
BN Army // 13th Mountain Division 